The present invention relates generally to structural machine components subjected to flexural and torsional loads, and more specifically, to a hollow bicycle crank arm of improved strength-to-weight ratio and reliability.
When a bicycle rider exerts a force on a crank arm, he applies a bending moment that tends to flex it into an arc. A transverse shear (beam shear) force also results from the pedaling force. Because it is laterally offset from the arm, the pedaling force also tends to twist the arm about its long axis. The applied bending moment varies from near-zero at the pedal to a maximum value at the crank spindle. This can cause reliability problems for any joints or welds that are near the crank spindle.
The need to reduce the weight of bicycle components, including crank arms, has resulted in several crank designs that are tubular, or hollow in the central portion. The optimal configuration may be seen to comprise a central, thin-wall tubular portion monolithic with substantially solid end portions that serve as mounting-bosses for a crank spindle and a pedal. The transitions from the solid end portions to the tubular portion are gradual and there are no sharp edges or comers. Sharp edges, corners, abrupt changes in material thickness and other geometric discontinuities induce stress concentrations. Stress concentrations significantly increase stress levels over nominal values, requiring extra material thickness to ensure reliability. A crank arm that is largely free of stress concentrations may have reduced material thickness and weight without any reduction in strength or reliability.
The optimal bicycle crank arm configuration is readily apparent in biological systems subjected to similar structural loads. For example, a human femur is continually subjected to flexure and torsion during walking, running, lifting objects, etc. A cross-section of a femur reveals dense, compact bone at the hip and knee condyles and around the outer perimeter of the central shaft, with porous cancellous bone and non-structural marrow in the shaft's interior region. The optimal crank arm configuration is analogous to a femur, and thus biomimetic. There has been great interest lately, in a wide range of applications, to adapt prima facie optimal biological systems to man-made biomimetic articles. There have been various attempts to economically produce an optimal hollow crank arm.